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country club at the highlands - NBX Soluciones

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Divide by 6: \( w = \frac{44}{6} = \frac{22}{3} \approx 7.33 \) meters.

📌 Then \( l = 2(\frac{22}{3}) + 5 = \frac{44}{3} + 5 = \frac{59}{3} \approx 19.67 \) meters.

📌 #### Width: 7.33 meters, Length: 19.67 meters

📌 A company’s profit in thousands of dollars is modeled by \( P(x) = -2x^2 + 20x - 30 \), where \( x \) is the number of units sold in hundreds. What is the maximum profit, and how many units maximize it?

📌 This is a quadratic function in vertex form. The vertex occurs at \( x = -\frac{b}{2a} = -\frac{20}{2(-2)} = 5 \).

📌 So maximum profit occurs when \( x = 5 \), i.e., 500 units.

📌 Plug into \( P(x) \): \( P(5) = -2(25) + 20(5) - 30 = -50 + 100 - 30 = 20 \).

📌 Thus, maximum profit is $20,000.

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